Sankhya: The Indian Journal of Statistics
1995, Volume 57, Series A, Pt. 2, pp. 316--332
A NEAREST NEIGHBOUR CLASSIFICATION RULE FOR MULTIPLE OBSERVATIONS BASED ON A SUB-SAMPLE APPROACH
S.C. BAGUI, The University of West Florida
K.L. MEHRA, University of Alberta
M.S. RAO, Osmania University
SUMMARY. In this paper, a 1-nearest neighbour (NN) classification rule for classifying $m$ multiple observations into one of $s$ populations is proposed by suitably sub-grouping the training sample observations. This classification rule generalizes the one by Cover and Hart (1967) for a single observation to $m$ multiple observations. The asymptotic risk of the proposed rule is derived and the bounds thereon in terms of the corresponding Bayes risk are shown to be parallel to those obtained by Cover and Hart (1967) for the case $m = 1$. A proposed cross-validation type estimator of the asymptotic risk is shown to be asymptotically unbiased and consistent. Further, the results of a Monte Carlo study are reported to assess the performance of the proposed
rule and to compare it with that of the 1st-stage rank nearest neighbour (RNN) rule for multiple observations (Bagui, 1989) in small sample situations.
AMS (1990) subject classification. Primary 62H30, secondary 62F15, 62G10, 62G20.
Key words and phrases. Bayes risk, classification, discrimination, discrimination, misclassification, nearest neighbor, repeated measurements.
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